Chapter 4.3, Problem 13AYU

To determine

To find: The remaining zeros of the polynomial function $f\left(x\right)$ whose coefficients are real numbers.

Answer to Problem 13AYU

$\text{Complex conjugate }–i\text{ is the remaining zero of polynomial function }f\left(x\right)$.

Explanation of Solution

Given:

Degree $=4$, zeros $=i,2,-2$.

Since the degree $=4$ there will be 4 real zeros.

Since $i$ is the complex zero of the polynomial function $f\left(x\right)$ and $f\left(x\right)$ has coefficients that are real numbers Complex zero appear as conjugate pairs.

By the conjugate pair theorem $i$ is the complex zero of the polynomial function $f\left(x\right)$.

The complex conjugate of $i=-i$ is also the zero of polynomial function $f\left(x\right)$.